Born in Moscow, in 1938 he entered Moscow State University. Following evacuation in 1941 during the "Great Patriotic War", he graduated in Ashkhabad, in today's Turkmenistan. He was then assigned laboratory work in Ulyanovsk. He returned to Moscow in 1945 to study at the Theoretical Department of FIAN (the Physical Institute of the USSR Academy of Sciences). He received his Ph.D. in 1947.

On World War II's end, Sakharov researched cosmic rays. In mid-1948 he participated in the Soviet atomic bomb project under Igor Kurchatov. The first Soviet atomic device was tested on August 29, 1949. After moving to Sarov in 1950, Sakharov played a key role in the next stage, the development of the hydrogen bomb. The first Soviet device was tested on August 12, 1953. In 1953 he received D.Sc. degree, was elected a full member of the USSR Academy of Sciences, and was awarded the first of his three Hero of Socialist Labor titles. Sakharov continued to work at Sarov, helping on the first genuine Soviet H-bombs, tested in 1955, and the 50MT 'Tsar Bomba' of October 1961, the most powerful device ever exploded.

He also proposed an idea for a controlled fusion reactor, the tokamak, that is still the basis for the majority of work in the area. Sakharov, in association with Igor E. Tamm, proposed confining extremely hot ionized plasma by torus shaped magnetic fields for controlling thermonuclear fusion. This led to the development of the tokamak device.

From the late-1950s Sakharov had become concerned about the moral and political implications of his work. Politically active during the 1960s, Sakharov was against nuclear proliferation. Pushing for the end of atmospheric tests he played a role in the 1963 Partial Test Ban Treaty, signed in Moscow. In 1965 he returned to fundamental science and began working on cosmology but continued to oppose political discrimination.

The major turn in Sakharov’s political evolution started in 1967, when anti-ballistic missile defense became a key issue in U.S.-Soviet relations. In a secret detailed letter to the Soviet leadership of July 21, 1967, Sakharov explains the need to “take the Americans at their word” and accept their proposal “for a bilateral rejection by the USA and the USSR of the development of antiballistic missile defense”, because otherwise an arms race in this new technology would increase the likelihood of nuclear war. He also asked a permission to publish his article manuscript (accompanied the letter) in a newspaper to explain the tricky danger of this kind of defense. The government ignored his letter and refused to let him initiate a public discussion of ABM in the Soviet press.

In May 1968 he completed an essay, Reflections on Progress, Peaceful Coexistence, and Intellectual Freedom, where the anti-ballistic missile defense is featured as a major threat of world nuclear war. After this essay was circulated in samizdat and then published outside the Soviet Union, Sakharov was banned from all military-related research and Sakharov returned to FIAN to study fundamental theoretical physics. In 1970 he was one of the founders of the Moscow Human Rights Committee and came under increasing pressure from the regime. He married a fellow human rights activist Yelena Bonner in 1972.

In 1973 he was nominated for the Nobel Peace Prize. He won the prize in 1975, although he was not allowed to leave the USSR to collect it. Sakharov's ideas on social development led him to put forward the principle of human rights as a new basis of all politics. In his works he declared that "the principle "what is not prohibited is allowed" should be understood literally", denying the importance and validity of all moral or cultural norms not codified in the laws. He was arrested on January 22, 1980 following his public protests against the invasion of Afghanistan in 1979 and was sent to internal exile to a city of Gorki, a closed city that was out of reach for foreigners.

Between 1980 to 1986, Sakharov was kept under tight Soviet police surveillance. In his memoirs he mentions that their apartment in Gorky was repeatedly subjected to searches and heists. He remained isolated but unrepentant until December 1986 when he was allowed to return to Moscow as Mikhail Gorbachev initiated the policies of perestroika and glasnost.

He helped to initiate the first independent legal political organizations and became prominent in the Soviet Union's growing political opposition. In April 1989, Sakharov was elected to the new parliament, the All-Union Congress of Peoples' Deputies and co-led the democratic opposition.

Sakharov died of a heart attack in 1989, and was interred in the Vostryakovskoye Cemetery in Moscow.

The Sakharov Prize for Freedom of Thought, established in 1985 and awarded annually by the European Parliament for people and organizations dedicated to human rights and freedoms, was named in his honor.

Sakharov and the "Sakharov Drive" were featured in Arthur C. Clarke's novel 2010: Odyssey Two. One of the Enterprise-D shuttlecraft in Star Trek: The Next Generation was also named for him.